Tunneling conductance for Majorana fermions in spin-orbit coupled semiconductor-superconductor heterostructures using superconducting leads

TL;DR

This paper investigates how superconducting leads affect tunneling conductance measurements of Majorana fermions in spin-orbit coupled semiconductor-superconductor heterostructures, highlighting the suppression of thermal broadening and the unique oscillation signatures.

Contribution

It provides a detailed analysis of tunneling spectra with superconducting leads, revealing the impact of Majorana splitting energy and contrasting signatures with metallic leads.

Findings

Majorana splitting energy causes peak broadening in finite wires.

Superconducting leads suppress temperature broadening effects.

Oscillations of quasi-Majorana peaks occur around bias equal to the lead gap.

Abstract

It has been recently pointed out that the use of a superconducting (SC) lead instead of a normal metal lead can suppress the thermal broadening effects in tunneling conductance from Majorana fermions, helping reveal the quantized conductance of $2e^2/h$. In this paper we discuss the specific case of tunneling conductance with SC leads of spin-orbit coupled semiconductor-superconductor (SM-SC) heterostructures in the presence of a Zeeman field, a system which has been extensively studied both theoretically and experimentally using a metallic lead. We examine the $dI/dV$ spectra using a SC lead for different sets of physical parameters including temperature, tunneling strength, wire length, magnetic field, and induced SC pairing potential in the SM nanowire. We conclude that in a finite wire the Majorana splitting energy $\Delta E$, which has non-trivial dependence on these physical parameters, remains responsible for the $dI/dV$ peak broadening, even when the temperature broadening is suppressed by the SC gap in the lead. In a finite wire the signatures of Majorana fermions with a SC lead are oscillations of quasi-Majorana peaks about bias $V=\pm\Delta_{\text{lead}}$, in contrast to the case of metallic leads where such oscillations are about zero bias. Our results will be useful for analysis of future experiments on SM-SC heterostructures using SC leads.